An angle modulated signal is given as \(x_c(t)=20 \cos \left[200 \pi t+\frac{\pi}{4}\right] \). What is the instantaneous frequency?

Given that \( Xc=20cos(200\pi t+ \frac{\pi} {4}) \)

Angle modulation is the process in which the total phase angle of the carrier wave is varied in accordance with the instantaneous amplitude of the message signal.

Here, instantaneous frequency is the rate of change of phase with respect to time.

f₁=\(\)\( \frac{1\:d\theta(t)} {2\pi\: dt} \)

 =\(\frac {1}{2 \pi} [200\pi]\)

\(=100Hz\)

Here, option 2 is correct.